
optimization
A 150 room hotel will rent all of its room if it charges $40 per room. The manager knows that for each $2 dollar increase per room, eight fewer room will be rented per night. What rent would maximize the revenue per night?
I'm having trouble setting up the equation.
I said w= each $2 dollar increase
so revenue= (1508w)(40+w)
but this comes out wrong. I know w should =0, right. Any help would be great

Say we do a 2 dollar increase. According to your definition, w = 1. Therefore the hotel will rent out 1508*1 = 142 rooms for 40+1=41 dollars per room (!).
Do you see how you should correct your formula now?